CancellationAbelianMonoid

catdef.spad line 166 [edit on github]

This is an AbelianMonoid with the cancellation property, i.e. `` a+b = a+c => b=c ``. This is formalised by the partial subtraction operator, which satisfies the axioms listed below:

0: %

from AbelianMonoid

*: (NonNegativeInteger, %) -> %

from AbelianMonoid

*: (PositiveInteger, %) -> %

from AbelianSemiGroup

+: (%, %) -> %

from AbelianSemiGroup

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm

from CoercibleTo OutputForm

latex: % -> String

from SetCategory

opposite?: (%, %) -> Boolean

from AbelianMonoid

sample: %

from AbelianMonoid

subtractIfCan: (%, %) -> Union(%, failed)

subtractIfCan(x, y) returns an element z such that z+y=x or “failed” if no such element exists.

zero?: % -> Boolean

from AbelianMonoid

AbelianMonoid

AbelianSemiGroup

BasicType

CoercibleTo OutputForm

SetCategory